A Weighty Problem

After Sammy reluctantly freed his erstwhile prisoners they went their separate ways. Most of them, with only strength and fighting skill to recommend them, went off as a band to be mercenaries (or brigands, if they couldn't find work) in a neighboring country. Brian wasn't interested in such a life, though. He was actually a fairly law-abiding sort, for one thing, having only landed in prison for giving President Marco a real stumper of a puzzle.

Brian did need money, though. He was penniless, and dressed in little better than rags. He was also terribly hungry. The morning of the third day he followed some tantalizing smells over a hill, and found a little carnival going on. Of course he had no money, so he couldn't buy anything, but he wandered through looking at the sights and hoping for a windfall of some sort.

In the middle of the carnival an area was cordoned off, and fifty bags were sitting in a line. Brian learned that there was a contest on: one of the fifty bags contained gold coins; the other forty-nine contained counterfeit coins. Each bag held sixty coins. All of the coins looked identical, and to a person they felt identical, but the real coins weighed one milligram more than the counterfeit coins, which each weighed one gram. The area also held a large, ornate scale accurate to within one milligram. The challenge was to figure out, in a single weighing, which of the bags contained the real coins. The first person to answer correctly won the bag of gold coins. Anyone who answered incorrectly, though, was to do hard labor for the local miller who had sponsored the contest.

A number of people had already tried and failed, and the crowd had grown cautious. A couple were scribbling in the dust or manipulating heaps of pebbles, trying to gain an insight. Sammy studied the setup for a time. An hour later he left the carnival with the bag of gold and a couple hired guards to seek further fortune. How did he solve the problem?

Solution